The dumping of the Gibson inquiry may not be mourned by many, but it is likely to mean that the truth about who was ultimately responsible for Britain's involvement in the abuse and secret rendition of dissidents and terror suspects abroad will be suppressed for even longer, perhaps for ever.

As more and more evidence emerged about how British officials connived in the capture and interrogation of detainees, more questions were raised about who knew and in what circumstances.

Ministers and former ministers (most of the cases came under Labour's watch), and security and intelligence officials, brushed aside all questions about their roles, saying they would talk only to Gibson.

Both Tony Blair and the former foreign secretary Jack Straw distanced themselves from the actions which led to individuals, including Libyans once linked to extremist groups, being abused and tortured.

Whitehall sources insist MI6 specifically sought ministerial authorisation for the rendition of the Libyans – Abdul Hakim Belhaj and Sami al-Saadi – and had sought assurances from Muammar Gaddafi that the men and their families would not be abused. Just wait for Gibson, Whitehall insisted.

The Gibson inquiry became a convenient pigeonhole. David Cameron established the inquiry in July 2010, honouring a pre-election pledge for a "fully independent" judge-led inquiry into allegations of British collusion in the abusive treatment of terror suspects.

Hard evidence of British collusion emerged three years ago during high court hearings into the treatment of Binyam Mohamed, an Ethiopian-born UK resident seized in Pakistan early in 2002, tortured in Morocco and flown to Guantánamo Bay via Afghanistan's infamous Bagram jail.

Nine British residents and citizens sued for compensation, alleging MI5 and MI6 involvement in their rendition to Guantánamo. They settled out of court because MI5 and MI6, vigorously backed by the Labour government, did not want any incriminating intelligence being disclosed in court. Labour's then foreign secretary, David Miliband, had already succeeded in blocking the release of all but a fragment of CIA information being revealed by the courts during the Mohamad hearings.

Miliband's predecessor, Jack Straw, initially denied any British role in CIA rendition flights. We still do not know what he knew about the rendering of the two Libyans to Tripoli in the spring of 2004, days before Blair celebrated, in a tent by the desert, a new relationship with Gaddafi following the Libyan leader's promise to abandon the procurement of weapons of mass destruction.

The Gibson inquiry had already been delayed by police investigations into an MI5 and MI6 officer. Unsurprisingly, the government has now pulled the plug after last week's revelation that the police are investigating UK involvement in the Libyan renditions.

A big question is whether the police will now interrogate former ministers as well as MI6 officers about the Libyan cases.

Kenneth Clarke, the justice secretary, told MPs on Wednesday that the government "fully intends to hold an independent, judge-led inquiry, once all police investigations have concluded, to establish the full facts and draw a line under these issues".

The further question is whether all evidence about intelligence to this future inquiry will be heard in secret, as the Gibson inquiry intended, in a move that human rights groups and the detainees' lawyers said undermined its credibility.